1. A. (20p) Give a Big-O estimate that is as good as possible for each of the following functions.
i. (n^3 + n)(logn + n)
ii. (n + 1000)(logn + 1)
B. (15p) If these are complexities of algorithms that solve the same problem, which one would you
prefer? Why?
C. (15p) Considering the Big-O complexity, how many times is your choice faster with respect to the
other solution for an input size of 2^16?
Note: The base of logarithm is 2
A.i.
ii. B. The second estimate of the complexity is preferable, as its growth is much more slower.
C. If n=216 then
,
and the second estimate of the complexity is 244 times better.
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